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5
Easy Functional Equation with one variable
Easy Functional Equation with one variable
Source:
April 25, 2011
function
algebra proposed
algebra
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that
∀
x
∉
{
−
1
,
1
}
\forall x\notin\{-1,1\}
∀
x
∈
/
{
−
1
,
1
}
holds:
f
(
x
−
3
x
+
1
)
+
f
(
3
+
x
1
−
x
)
=
x
\displaystyle{f\Big(\frac{x-3}{x+1}\Big)+f\Big(\frac{3+x}{1-x}\Big)=x}
f
(
x
+
1
x
−
3
)
+
f
(
1
−
x
3
+
x
)
=
x
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